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gp - PARI calculator

gp[--stacksize|-sstacksize] [--primelimit|-pprimelimit] [--emacs] [-f|--fast] [-q|--quiet] [--help] [--test] [--texmacs] [--version] [--version-short] [ file1 file2 ...]

Invokes the PARI-GP calculator, loading the file1, file2, ... (written in the GP language) on startup. gp is an advanced programmable calculator, which computes symbolically as long as possible, numerically where needed, and contains a wealth of number-theoretic functions (elliptic curves, class field theory...). It can be programmed with the GP scripting language. Its basic data types are numbers integers, real numbers, exact rational numbers, algebraic numbers,p-adic numbers, modular integers (integers modulon), complex numbers, polynomials, rational functions, and power series, integral binary quadratic forms, matrices, vectors, and lists, character strings, and recursive combinations of these.

Command line options are availaible in both short form (-f) and POSIX- like (--fast). Numeric arguments can be followed by a modifierk,MorGat the user’s convenience; in that case the argument is multiplied by 10^3, 10^6, or 10^9 respectively.-f,--fastFast start (or factory settings). Do not read.gprc(see below) upon startup.-p,--primelimitlimitUpon startup, gp computes a table of small primes used in number-theoretic applications. Ifprimelimitis set, the table include primes up to that bound instead of the default. Unreasonably high values will considerably increase startup time. Exceedingly small values will cause some number-theoretic functions to fail with the message "not enough precomputed primes".-q,--quietQuiet mode. Don’t print headers or history numbers, don’t say goodbye.-s,--stacksizelimitSize of gp internal stack allocated on startup. When gp runs out of space, it interrupts the current computation and raises astackoverflowexception. If this occurs frequently, start with a bigger stack. The stack size can also be increased from within gp, usingdefault(parisize,...);it may be convenient to setstacksizefrom your.gprc.Note that computations with asmallerstack may be more efficient due to better data locality. Most computations should need less than 20MB.--emacsgp can be run in anEmacsshell (see GP User’s manual for details). This flag is then required for smooth interaction with the relevantEmacspackage (pari.el). It is set automatically by the pari.el package, and will produce nice display oddities if you set it outside of anEmacssession.--helpprint a summary of available command-line options.--testrun gp in test mode: suppress printing of history numbers and wrap long output lines (to get readable diff output). For benches only.--texmacsgp can be run from aTeXmacsfrontend. This flag is set by TeXmacs, to enable special purpose communication channels. Do not set it yourself.--versionoutput version info (banner) then exit.--version-shortoutput version number then exit.

?to get online help.??to get extended online help (more precisely, to call the external help program,gphelpby default)quit(or \q), orEOF(Ctrl-D) to quitgp. The following works only when gp was linked with GNUreadlinelibrary: arrow keys for editing and viewing the input history.TABfor automatic completion

The following material is included in the standard distribution (originally in TeX format):TheUsersGuidetoPARI/GP(users.dvi)TheUsersGuidetothePARIlibrary(library.dvi)PARI/GP,atutorial(tutorial.dvi)PARI/GPreferencecard(refcard.ps): 4 pages, based on an earlier version by Joseph H. Silverman.pariemacs.txtexplains the use of the pari.el package, and how to customize it (prompt, colors).

gpmain executable$HOME/.gprc(or $GPRC if set) read at beginning of execution by eachgpshell. A default gprcgprc.dftis provided with the distribution. If this file cannot be found,/etc/gprcis checked instead.pari.logdefault logfile (can be changed in.gprcor interactively usingdefault())pari.psdefault psfile used for postscript output (as above)gphelpdefault external help program (as above)pari.elelisp package to run pari in anEmacsshell. Must be loaded from your.emacsfile.*.gpGP programs

$GPRCplace to look for the user’s gprc file (before $HOME/.gprc, ./gprc, and /etc/gprc in this order).$GP_DATA_DIRdirectory containing precomputed data. For now, the Galois resolvents files in directorygaldata/,needed by thepolgaloisfunction, in degrees 8 to 11.$GPHELPname of the external help program invoked by ?? and ??? shortcuts.$GPTMPDIRname of the directory where temporary files will be generated.

PARI’s home page resides athttp://pari.math.u-bordeaux.fr/

There are three mailing lists devoted to the PARI/GP package (run courtesy of Dan Bernstein), and most feedback should be directed to those. They are: -pari-announce(moderated): for us to announce major version changes. -pari-dev:for everything related to the development of PARI, including suggestions, technical questions, bug reports or patch submissions. -pari-users:for everything else. To subscribe, send empty messages respectively to pari-announce-subscribe@list.cr.yp.to pari-users-subscribe@list.cr.yp.to pari-dev-subscribe@list.cr.yp.to

Bugs should be submitted online to our Bug Tracking System, available from PARI’s home page, or directly from the URLhttp://pari.math.u-bordeaux.fr/Bugs/Further instructions can be found on that page.

Despite the leading G, GP has nothing to do with GNU. The first version was originally called GPC, for Great Programmable Calculator. For some reason, the trailing C was eventually dropped. PARI has nothing to do with the French capital. The name is a pun about the project’s early stages when the authors started to implement a library for "Pascal ARIthmetic" in the PASCAL programming language (they quickly switched to C). For the benefit of non-native French speakers, here’s a slightly expanded explanation:BlaisePascal(1623-1662) was a famous French mathematician and philosopher who was one of the founders of probability and devised one of the first "arithmetic machines". He once proposed the following "proof" of the existence of God for the unbelievers: whether He exists or not I lose nothing by believing in Him, whereas if He does and I misbehave... This is the so-called "pari de Pascal" (Pascal’s Wager). Note that PARI also means "fairy" in Persian.

PARI was originally written by Christian Batut, Dominique Bernardi, Henri Cohen, and Michel Olivier in Laboratoire A2X (Universite Bordeaux I, France), and was maintained by Henri Cohen up to version 1.39.15 (1995), and by Karim Belabas since then. A great number of people have contributed to the successive improvements which eventually resulted in the present version. See the AUTHORS file in the distribution.

dvips(1),emacs(1),gap(1),ghostview(1),gphelp(1),maple(1),perl(1),readline(3),tex(1),texmacs(1),xdvi(1)

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. 10 August 2004 GP(1)